Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Distortion of Dimension under Quasiconformal Mappings

Quasiconformal mappings are natural generalizations of conformal mappings. They are homeomorphisms with 'bounded distortion' of which there exist several approaches. In this work we study dimension distortion properties of quasiconformal mappings both in the plane and in higher dimensional Euclidean setting. The thesis consists of a summary and three research articles. A basic property of quasiconformal mappings is the local Hölder continuity. It has long been conjectured that this regularity holds at the Sobolev level (Gehring's higher integrabilty conjecture). Optimal regularity would also provide sharp bounds for the distortion of Hausdorff dimension. The higher integrability conjecture was solved in the plane by Astala in 1994 and it is still open in higher dimensions. Thus in the plane we have a precise description how Hausdorff dimension changes under quasiconformal deformations for general sets. The first two articles contribute to two remaining issues in the planar theory. The first one concerns distortion of more special sets, for rectifiable sets we expect improved bounds to hold. The second issue consists of understanding distortion of dimension on a finer level, namely on the level of Hausdorff measures. In the third article we study flatness properties of quasiconformal images of spheres in a quantitative way. These also lead to nontrivial bounds for their Hausdorff dimension even in the n-dimensional case.

Finitary Abstract Elementary Classes

The research in model theory has extended from the study of elementary classes to non-elementary classes, i.e. to classes which are not completely axiomatizable in elementary logic. The main theme has been the attempt to generalize tools from elementary stability theory to cover more applications arising in other branches of mathematics. In this doctoral thesis we introduce finitary abstract elementary classes, a non-elementary framework of model theory. These classes are a special case of abstract elementary classes (AEC), introduced by Saharon Shelah in the 1980's. We have collected a set of properties for classes of structures, which enable us to develop a 'geometric' approach to stability theory, including an independence calculus, in a very general framework. The thesis studies AEC's with amalgamation, joint embedding, arbitrarily large models, countable Löwenheim-Skolem number and finite character. The novel idea is the property of finite character, which enables the use of a notion of a weak type instead of the usual Galois type. Notions of simplicity, superstability, Lascar strong type, primary model and U-rank are inroduced for finitary classes. A categoricity transfer result is proved for simple, tame finitary classes: categoricity in any uncountable cardinal transfers upwards and to all cardinals above the Hanf number. Unlike the previous categoricity transfer results of equal generality the theorem does not assume the categoricity cardinal being a successor. The thesis consists of three independent papers. All three papers are joint work with Tapani Hyttinen.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Turing and the Trans-Pacific Partnership: Intellectual Property, Public Health, and Access to Essential Medicines

A recent controversy in the United States over drug pricing by Turing Pharmaceuticals AG has raised larger issues in respect of intellectual property, access to medicines, and the Trans-Pacific Partnership (TPP). In August 2015, Turing Pharmaceuticals AG – a private biopharmaceutical company with offices in New York, the United States, and Zug, Switzerland - acquired the exclusive marketing rights to Daraprim in the United States from Impax Laboratories Incorporated. Martin Shkreli, Turing’s Founder and Chief Executive Officer, maintained: “The acquisition of Daraprim and our toxoplasmosis research program are significant steps along Turing’s path of bringing novel medications to patients with serious disorders, some of whom often go undiagnosed and untreated.” He emphasised: “We intend to invest in the development of new drug candidates that we hope will yield an even better clinical profile, and also plan to launch an educational effort to help raise awareness and improve diagnosis for patients with toxoplasmosis.” In September 2015, there was much public controversy over the decision of Martin Shkreli to raise the price of a 62 year old drug, Daraprim, from $US13.50 to $US750 a pill. The drug is particularly useful in respect to the treatment and prevention of malaria, and in the treatment of infections in individuals with HIV/AIDS. Daraprim is listed on the World Health Organization’s (WHO) List of Essential Medicines. In the face of much criticism, Martin Shkreli has said that he will reduce the price of Daraprim. He observed: “We've agreed to lower the price on Daraprim to a point that is more affordable and is able to allow the company to make a profit, but a very small profit.” He maintained: “We think these changes will be welcomed.” However, he has been vague and ambiguous about the nature of the commitment. Notably, the lobby group, Pharmaceutical Research and Manufacturers of America (PhARMA), disassociated itself from the claims of Turing Pharmaceuticals. The group said: “PhRMA members have a long history of drug discovery and innovation that has led to increased longevity and improved lives for millions of patients.” The group noted: “Turing Pharmaceutical is not a member of PhRMA and we do not embrace either their recent actions or the conduct of their CEO.” The biotechnology peak body Biotechnology Industry Organization also sought to distance itself from Turing Pharmaceuticals. A hot topic: United States political debate about access to affordable medicines This controversy over Daraprim is unusual – given the age of drug concerned. Daraprim is not subject to patent protection. Nonetheless, there remains a monopoly in respect of the marketplace. Drug pricing is not an isolated problem. There have been many concerns about drug pricing – particularly in respect of essential medicines for HIV/AIDS, tuberculosis, and malaria. This recent controversy is part of a larger debate about access to affordable medicines. The dispute raises larger issues about healthcare, consumer rights, competition policy, and trade. The Daraprim controversy has provided impetus for law reform in the US. US Presidential Candidate Hillary Clinton commented: “Price gouging like this in this specialty drug market is outrageous.” In response to her comments, the Nasdaq Biotechnology Index fell sharply. Hillary Clinton has announced a prescription drug reform plan to protect consumers and promote innovation – while putting an end to profiteering. On her campaign site, she has emphasised that “affordable healthcare is a basic human right.” Her rival progressive candidate, Bernie Sanders, was also concerned about the price hike. He wrote a letter to Martin Shkreli, complaining about the price increase for the drug Daraprim. Sanders said: “The enormous, overnight price increase for Daraprim is just the latest in a long list of skyrocketing price increases for certain critical medications.” He has pushed for reforms to intellectual property to make medicines affordable. The TPP and intellectual property The Daraprim controversy and political debate raises further issues about the design of the TPP. The dispute highlights the dangers of extending the rights of pharmaceutical drug companies under intellectual property, investor-state dispute settlement, and drug administration. Recently, the civil society group Knowledge Ecology International published a leaked draft of the Intellectual Property Chapter of the TPP. Knowledge Ecology International Director, James Love, was concerned the text revealed that the US “continues to be the most aggressive supporter of expanded intellectual property rights for drug companies.” He was concerned that “the proposals contained in the TPP will harm consumers and in some cases block innovation.” James Love feared: “In countless ways, the Obama Administration has sought to expand and extend drug monopolies and raise drug prices.” He maintained: “The astonishing collection of proposals pandering to big drug companies make more difficult the task of ensuring access to drugs for the treatment of cancer and other diseases and conditions.” Love called for a different approach to intellectual property and trade: “Rather than focusing on more intellectual property rights for drug companies, and a death-inducing spiral of higher prices and access barriers, the trade agreement could seek new norms to expand the funding of medical research and development (R&D) as a public good, an area where the US has an admirable track record, such as the public funding of research at the National Institutes of Health (NIH) and other federal agencies.” In addition, there has been much concern about the Investment Chapter of the TPP. The investor-state dispute settlement regime would enable foreign investors to challenge government policy making, which affected their investments. In the context of healthcare, there is a worry that pharmaceutical drug companies will deploy their investor rights to challenge public health measures – such as, for instance, initiatives to curb drug pricing and profiteering. Such concerns are not merely theoretical. Eli Lilly has brought an investor action against the Canadian Government over the rejection of its drug patents under the investor-state dispute settlement regime of the North American Free Trade Agreement (NAFTA). The Health Annex to the TPP also raises worries that pharmaceutical drug companies will able to object to regulatory procedures in respect of healthcare. It is disappointing that the TPP – in the leaks that we have seen – has only limited recognition of the importance of access to essential medicines. There is a need to ensure that there are proper safeguards to provide access to essential medicines – particularly in respect of HIV/AIDs, malaria, and tuberculosis. Moreover, there must be protection against drug profiteering and price gouging in any trade agreement. There should be strong measures against the abuse of intellectual property rights. The dispute over Turing Pharmaceuticals AG and Daraprim is an important cautionary warning in respect of some of the dangers present in the secret negotiations in respect of the TPP. There is a need to preserve consumer rights, competition policy, and public health in trade negotiations over an agreement covering the Pacific Rim.

Save Left Shark: Katy Perry, Intellectual Property, and 3D Printing

There has been much interest in how intellectual property law, policy and practice will adapt to the emergence of 3D printing and the maker movement. Intellectual property lawyers will have to grapple with the impact of additive manufacturing upon a variety of forms of intellectual property — including copyright law, trade mark law, designs law, patent law and trade secrets. The disruptive technology of 3D printing will both pose opportunities and challenges for legal practitioners and policy makers.A performance by pop princess Katy Perry at the 2015 Super Bowl has sparked a public controversy over intellectual property, internet memes and 3D printing.

Account of Isaac and Abraham de Peyster vs. Isaac Seixas and other papers

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On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Contract with John Moore for building house on Mill Street

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Digitaalisten teosten maailmanlaajuinen rekisteröinti ja käyttömaksujen kerääminen internetissä

The vastly increased popularity of the Internet as an effective publication and distribution channel of digital works has created serious challenges to enforcing intellectual property rights. Works are widely disseminated on the Internet, with and without permission. This thesis examines the current problems with licence management and copy protection and outlines a new method and system that solve these problems. The WARP system (Works, Authors, Royalties, and Payments) is based on global registration and transfer monitoring of digital works, and accounting and collection of Internet levy funded usage fees payable to the authors and right holders of the works. The detection and counting of downloads is implemented with origrams, short and original parts picked from the contents of the digital work. The origrams are used to create digests, digital fingerprints that identify the piece of work transmitted over the Internet without the need to embed ID tags or any other easily removable metadata in the file.

Mikä on ihme ja mitä ihmeistä voidaan tietää? : Keskustelu ihmeistä uusimmassa englanninkielisessä uskonnonfilosofiassa

What is a miracle and what can we know about miracles? A discussion of miracles in anglophone philosophy of religion literature since the late 1960s. The aim of this study is to systematically describe and philosophically examine the anglophone discussion on the subject of miracles since the latter half of the 1960s. The study focuses on two salient questions: firstly, what I will term the conceptual-ontological question of the extent to which we can understand miracles and, secondly, the epistemological question of what we can know about miracles. My main purpose in this study is to examine the various viewpoints that have been submitted in relation to these questions, how they have been argued and on what presuppositions these arguments have been based. In conducting the study, the most salient dimension of the various discussions was found to relate to epistemological questions. In this regard, there was a notable confrontation between those scholars who accept miracles and those who are sceptical of them. On the conceptual-ontological side I recognised several different ways of expressing the concept of miracle . I systematised the discussion by demonstrating the philosophical boundaries between these various opinions. The first and main boundary was related to ontological knowledge. On one side of this boundary I placed the views which were based on realism and objectivism. The proponents of this view assumed that miraculousness is a real property of a miraculous event regardless of how we can perceive it. On the other side I put the views which tried to define miraculousness in terms of subjectivity, contextuality and epistemicity. Another essential boundary which shed light on the conceptual-ontological discussion was drawn in relation to two main views of nature. The realistic-particularistic view regards nature as a certain part of reality. The adherents of this presupposition postulate a supernatural sphere alongside nature. Alternatively, the nominalist-universalist view understands nature without this kind of division. Nature is understood as the entire and infinite universe; the whole of reality. Other, less important boundaries which shed light on the conceptual-ontological discussion were noted in relation to views regarding the laws of nature, for example. I recognised that the most important differences between the epistemological approaches were in the different views of justification, rationality, truth and science. The epistemological discussion was divided into two sides, distinguished by their differing assumptions in relation to the need for evidence. Adherents of the first (and noticeably smaller) group did not see any epistemological need to reach a universal and common opinion about miracles. I discovered that these kinds of views, which I called non-objectivist, had subjectivist and so-called collectivist views of justification and a contextualist view of rationality. The second (and larger) group was mainly interested in discerning the grounds upon which to establish an objective and conclusive common view in relation to the epistemology of miracles. I called this kind of discussion an objectivist discussion and this kind of approach an evidentialist approach. Most of the evidentialists tried to defend miracles and the others attempted to offer evidence against miracles. Amongst both sides, there were many different variations according to emphasis and assumption over how they saw the possibilities to prove their own view. The common characteristic in all forms of evidentialism was a commitment to an objectivist notion of rationality and a universalistic notion of justification. Most evidentialists put their confidence in science in one way or another. Only a couple of philosophers represented the most moderate version of evidentialism; they tried to remove themselves from the apparent controversy and contextualised the different opinions in order to make some critical comments on them. I called this kind of approach a contextualising form of evidentialism. In the final part of the epistemological chapter, I examined the discussion about the evidential value of miracles, but nothing substantially new was discovered concerning the epistemological views of the authors.

Committee report

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Minutes of the congregation

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Zapys zemelʹnyĭ Na pravo korystovanni︠a︡ zemli︠u︡, shcho znakhoditʹsi︠a︡ v Odeskoï guberni Peryletravenʹsʹkyĭ okruzi Kantakuzenʹsʹy raʹoni pid nazvoi︠u︡ Trudovyshyĭ artilʹ Slava

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